Question
Download Solution PDFThe 11th term of an AP is 90 less than the first term. If the second term is 99, find the third term.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The 11th term of an AP is 90 less than the first term. The second term is 99.
Formula:
nth term of an AP, Tn = a + (n - 1)d, where ‘a’ is the first term, ‘n’ is the total number of terms and ‘d’ is the common difference.
Calculation:
Let the first term is ‘a’ and common difference is‘d’.
T2 = a + d = 99 ----(1)
According to question
T1 - T11 = 90
⇒ a - (a + 10d) = 90
⇒ - 10d = 90
d = - 9
From equation (1)
a + (- 9) = 99
⇒ a = 108
Third term T3 = a + 2d
⇒ 108 + 2 × - 9 = 108 - 18 = 90
∴ Required answer is 90.
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